Advanced Statistics: Alpha Attractor
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
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| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.024 | ||||
| SD | 0.049 | ||||
| Sharpe ratio (Glass type estimate) | 0.500 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.491 | ||||
| df | 38.000 | ||||
| t | 0.902 | ||||
| p | 0.186 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.596 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.590 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.602 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.583 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.202 | ||||
| Upside Potential Ratio | 3.249 | ||||
| Upside part of mean | 0.066 | ||||
| Downside part of mean | -0.042 | ||||
| Upside SD | 0.044 | ||||
| Downside SD | 0.020 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 29.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.490 | ||||
| Mean of criterion | 0.024 | ||||
| SD of predictor | 0.263 | ||||
| SD of criterion | 0.049 | ||||
| Covariance | -0.001 | ||||
| r | -0.114 | ||||
| b (slope, estimate of beta) | -0.021 | ||||
| a (intercept, estimate of alpha) | 0.035 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 37.000 | ||||
| t(b) | -0.695 | ||||
| p(b) | 0.754 | ||||
| t(a) | 1.120 | ||||
| p(a) | 0.135 | ||||
| Lowerbound of 95% confidence interval for beta | -0.082 | ||||
| Upperbound of 95% confidence interval for beta | 0.040 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.028 | ||||
| Upperbound of 95% confidence interval for alpha | 0.098 | ||||
| Treynor index (mean / b) | -1.160 | ||||
| Jensen alpha (a) | 0.035 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.023 | ||||
| SD | 0.048 | ||||
| Sharpe ratio (Glass type estimate) | 0.483 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.473 | ||||
| df | 38.000 | ||||
| t | 0.870 | ||||
| p | 0.195 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.613 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.572 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.619 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.565 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.132 | ||||
| Upside Potential Ratio | 3.166 | ||||
| Upside part of mean | 0.065 | ||||
| Downside part of mean | -0.042 | ||||
| Upside SD | 0.043 | ||||
| Downside SD | 0.020 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 29.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.449 | ||||
| Mean of criterion | 0.023 | ||||
| SD of predictor | 0.243 | ||||
| SD of criterion | 0.048 | ||||
| Covariance | -0.001 | ||||
| r | -0.104 | ||||
| b (slope, estimate of beta) | -0.021 | ||||
| a (intercept, estimate of alpha) | 0.032 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 37.000 | ||||
| t(b) | -0.638 | ||||
| p(b) | 0.736 | ||||
| t(a) | 1.063 | ||||
| p(a) | 0.147 | ||||
| Lowerbound of 95% confidence interval for beta | -0.086 | ||||
| Upperbound of 95% confidence interval for beta | 0.045 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.029 | ||||
| Upperbound of 95% confidence interval for alpha | 0.094 | ||||
| Treynor index (mean / b) | -1.123 | ||||
| Jensen alpha (a) | 0.032 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.026 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.016 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 39.000 | ||||
| Minimum | 0.973 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.005 | ||||
| Maximum | 1.057 | ||||
| Mean of quarter 1 | 0.997 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.025 | ||||
| Inter Quartile Range | 0.005 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.026 | ||||
| Mean of outliers low | 0.973 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.231 | ||||
| Mean of outliers high | 1.027 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.115 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 3.404 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.001 | ||||
| Quartile 3 | 0.014 | ||||
| Maximum | 0.027 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.001 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.027 | ||||
| Inter Quartile Range | 0.014 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.075 | ||||
| Compounded annual return (geometric extrapolation) | 0.070 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.558 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.558 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.642 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.024 | ||||
| SD | 0.051 | ||||
| Sharpe ratio (Glass type estimate) | 0.462 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.462 | ||||
| df | 861.000 | ||||
| t | 0.838 | ||||
| p | 0.201 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.619 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.543 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.619 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.542 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.825 | ||||
| Upside Potential Ratio | 5.775 | ||||
| Upside part of mean | 0.166 | ||||
| Downside part of mean | -0.142 | ||||
| Upside SD | 0.042 | ||||
| Downside SD | 0.029 | ||||
| N nonnegative terms | 137.000 | ||||
| N negative terms | 725.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 862.000 | ||||
| Mean of predictor | 0.527 | ||||
| Mean of criterion | 0.024 | ||||
| SD of predictor | 0.331 | ||||
| SD of criterion | 0.051 | ||||
| Covariance | 0.001 | ||||
| r | 0.043 | ||||
| b (slope, estimate of beta) | 0.007 | ||||
| a (intercept, estimate of alpha) | 0.020 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 860.000 | ||||
| t(b) | 1.265 | ||||
| p(b) | 0.103 | ||||
| t(a) | 0.710 | ||||
| p(a) | 0.239 | ||||
| Lowerbound of 95% confidence interval for beta | -0.004 | ||||
| Upperbound of 95% confidence interval for beta | 0.017 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.036 | ||||
| Upperbound of 95% confidence interval for alpha | 0.076 | ||||
| Treynor index (mean / b) | 3.546 | ||||
| Jensen alpha (a) | 0.020 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.022 | ||||
| SD | 0.051 | ||||
| Sharpe ratio (Glass type estimate) | 0.439 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.439 | ||||
| df | 861.000 | ||||
| t | 0.796 | ||||
| p | 0.213 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.642 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.520 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.642 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.519 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.775 | ||||
| Upside Potential Ratio | 5.710 | ||||
| Upside part of mean | 0.165 | ||||
| Downside part of mean | -0.142 | ||||
| Upside SD | 0.042 | ||||
| Downside SD | 0.029 | ||||
| N nonnegative terms | 137.000 | ||||
| N negative terms | 725.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 862.000 | ||||
| Mean of predictor | 0.473 | ||||
| Mean of criterion | 0.022 | ||||
| SD of predictor | 0.327 | ||||
| SD of criterion | 0.051 | ||||
| Covariance | 0.001 | ||||
| r | 0.045 | ||||
| b (slope, estimate of beta) | 0.007 | ||||
| a (intercept, estimate of alpha) | 0.019 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 860.000 | ||||
| t(b) | 1.312 | ||||
| p(b) | 0.095 | ||||
| t(a) | 0.677 | ||||
| p(a) | 0.249 | ||||
| Lowerbound of 95% confidence interval for beta | -0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.017 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.036 | ||||
| Upperbound of 95% confidence interval for alpha | 0.074 | ||||
| Treynor index (mean / b) | 3.214 | ||||
| Jensen alpha (a) | 0.019 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.006 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 862.000 | ||||
| Minimum | 0.980 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.040 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 118.000 | ||||
| Percentage of outliers low | 0.137 | ||||
| Mean of outliers low | 0.997 | ||||
| Number of outliers high | 143.000 | ||||
| Percentage of outliers high | 0.166 | ||||
| Mean of outliers high | 1.004 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.237 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | 0.303 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.004 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 31.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.004 | ||||
| Quartile 3 | 0.010 | ||||
| Maximum | 0.051 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.003 | ||||
| Mean of quarter 3 | 0.005 | ||||
| Mean of quarter 4 | 0.027 | ||||
| Inter Quartile Range | 0.009 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.097 | ||||
| Mean of outliers high | 0.048 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.337 | ||||
| VaR(95%) (moments method) | 0.028 | ||||
| Expected Shortfall (moments method) | 0.050 | ||||
| Extreme Value Index (regression method) | -0.143 | ||||
| VaR(95%) (regression method) | 0.025 | ||||
| Expected Shortfall (regression method) | 0.032 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.074 | ||||
| Compounded annual return (geometric extrapolation) | 0.069 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.342 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.576 | ||||
| Compounded annual return / Expected Shortfall lognormal | 10.746 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | NA | ||||
| Sharpe ratio (Hedges UMVUE) | NA | ||||
| df | NA | ||||
| t | NA | ||||
| p | NA | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.957 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.428 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | NA | ||||
| b (slope, estimate of beta) | NA | ||||
| a (intercept, estimate of alpha) | NA | ||||
| Mean Square Error | NA | ||||
| DF error | NA | ||||
| t(b) | NA | ||||
| p(b) | NA | ||||
| t(a) | NA | ||||
| p(a) | NA | ||||
| Lowerbound of 95% confidence interval for beta | NA | ||||
| Upperbound of 95% confidence interval for beta | NA | ||||
| Lowerbound of 95% confidence interval for alpha | NA | ||||
| Upperbound of 95% confidence interval for alpha | NA | ||||
| Treynor index (mean / b) | NA | ||||
| Jensen alpha (a) | NA | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -12492933348697024.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -12420719861132300.000 | ||||
| df | 130.000 | ||||
| t | -8833837887775228.000 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13930479873814932.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -10910959848449668.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.864 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.429 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | -0.000 | ||||
| r | -0.000 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -8731867361939502.000 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.044 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | 2669804175288894583551554561769472.000 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 0.000 | ||||
| Minimum | NA | ||||
| Quartile 1 | NA | ||||
| Median | NA | ||||
| Quartile 3 | NA | ||||
| Maximum | NA | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | NA | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | NA | ||||
| Mean of outliers high | NA | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | NA | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||